相关论文: Comparative Theory of Background Independence

In this work we study the deformations into Lie bialgebras of the three relativistic Lie algebras: de Sitter, Anti-de Sitter and Poincar\'e, which describe the symmetries of the three maximally symmetric spacetimes. These algebras represent…

A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…

We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical…

A new result of G. Cz\'edli states that for an ordered set $P$ with at least two elements and a group $G$, there exists a bounded lattice $L$ such that the ordered set of principal congruences of $L$ is isomorphic to $P$ and the…

We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…

Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…

In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in…

We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…

In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call $(\mathrm{tw},\omega)$-bounded. While $(\mathrm{tw},\omega)$-bounded graph classes are…

Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…

We discuss mimetic gravity theories with direct couplings between the curvature and higher derivatives of the scalar field, up to the quintic order, which were proposed to solve the instability problem for linear perturbations around the…

This Series of Articles provides a local resolution of this major longstanding foundational problem between QM and GR, or, more generally, between Background Dependent and Background Independent Physics. We focus on the classical version;…

The study of global deformations of Lie algebras is related to the problem of classification of simple Lie algebras over fields of small characteristic. The classification of finite-dimensional simple Lie algebras is complete over…

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the…

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…

The classification of one parameter local Coulomb branch solution of theories with eight supercharges is given by assuming that it is given by a genus $g$ fiberation of Riemann surfaces. The crucial point is the fact that certain conjugacy…

Self-supervision is recently surging at its new frontier of graph learning. It facilitates graph representations beneficial to downstream tasks; but its success could hinge on domain knowledge for handcraft or the often expensive trials and…

Given a family of world-sheet superconformal field theories related by marginal deformation, we can formulate superstring field theory based on any of these world-sheet theories. Background independence is the statement that these different…

In this diploma thesis we discuss the deformation theory of Lie algebroids and Dirac structures. The first chapter gives a short introduction to Dirac structures on manifolds as introduced by Courant in 1990. We also give some physical…